Dynamic properties of moderately concentrated magnetic liquids

On the basis of statistical analysis, we derive expressions for the dynamic susceptibility, magnetization relaxation times, and the effective rheological characteristics of a moderately concentrated homogeneous ferrocolloid consisting of identical spherical ferroparticles suspended in a Newtonian liquid. The magnetic moment of a particle is assumed constant and rigidly “frozen” into the body of the particle. We also estimate how the magnetodipole and hydrodynamic interactions of the particles influence the effective dynamic properties of the ferrocolloid. Zh. éksp. Teor. Fiz. 114, 892–909 (September 1998)     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. I. The Neutral System

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise, and oppositely charged adjacent particles may swap positions. The model depends on two parameters. Analytic calculations using quadratic algebras, inhomogeneous solutions of the mean-field equations, and Monte Carlo simulations suggest that the model has three phases: (1) a pure phase in which one has three pinned blocks of only positive or negative particles and vacancies and in which translational invariance is broken; (2) a mixed phase in which the current has a linear dependence on one parameter, but is independent of the other one and of the density of the charged particles; in this phase one has a bump and a fluid, the bump (condensate) containing positive and negative particles only, the fluid containing charged particles and vacancies uniformly distributed; and (3) the mixed phase is separated from the disordered phase by a second-order phase transition which has many properties of the Bose–Einstein phase transition observed in equilibrium. Various critical exponents are found.     

On the theory of phase transitions in magnetic fluids

Particles of magnetic fluids (ferrofluids), as is known from experiments, can condense to bulk dense phases at low temperatures (that are close to room temperature) in response to an external magnetic field. It is also known that a uniform external magnetic field increases the threshold temperature of the observed condensation, thus stimulating the condensation process. Within the framework of early theories, this phenomenon is interpreted as a classical gas-liquid phase transition in a system of individual particles involved in a dipole-dipole interaction. However, subsequent investigations have revealed that, before the onset of a bulk phase transition, particles can combine to form a chain cluster or, possibly, a topologically more complex heterogeneous cluster. In an infinitely strong magnetic field, the formation of chains apparently suppresses the onset of a gas-liquid phase transition and the condensation of magnetic particles most likely proceeds according to the scenario of a gas-solid phase transition with a wide gap between spinodal branches. This paper reports on the results of investigations into the specific features of the condensation of particles in the absence of an external magnetic field. An analysis demonstrates that, despite the formation of chains, the condensation of particles in this case can proceed according to the scenario of a gas-liquid phase transition with a critical point in the continuous binodal. Consequently, a uniform magnetic field not only can stimulate the condensation phase transition in a system of magnetic particles but also can be responsible for a qualitative change in the scenario of the phase transition. This inference raises the problem regarding a threshold magnetic field in which there occurs a change in the scenario of the phase transition.     

NEW APPROXIMATE PHASE FUNCTIONS FOR SCATTERING OF UNPOLARIZED LIGHT BY DIELECTRIC PARTICLES

We present two new phase functions, one for particles small compared to the wavelength of the scattering radiation and the other for particles large compared to the wavelength of the scattering radiation. These phase functions have been validated for the case of Mie scatterers. For small particles, the results of the new phase function are found to be identical with the Mie results. For large particles, comparison with the Mie results show that the phase function presented here is an extremely good approximation to the Mie phase function. We believe that these phase functions can be expediently used in problems relating to solutions of the radiative transfer equations.     

Depletion-induced biaxial nematic states of boardlike particles

With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid-crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.     

Liquid–liquid phase transition and anomalous diffusion in simulated liquid GeO2

We perform molecular dynamics (MD) simulation of diffusion in liquid GeO₂ at the temperatures ranged from 3000 to 5000 K and densities ranged from 3.65 to 7.90 g/cm³. Simulations were done in a model containing 3000 particles with the new interatomic potentials for liquid and amorphous GeO₂, which have weak Coulomb interaction and Morse-type short-range interaction. We found a liquid–liquid phase transition in simulated liquid GeO₂ from a tetrahedral to an octahedral network structure upon compression. Moreover, such phase transition accompanied with an anomalous diffusion of particles in liquid GeO₂ that the diffusion constant of both Ge and O particles strongly increases with increasing density (e.g. with increasing pressure) and it shows a maximum at the density around 4.95 g/cm³. The possible relation between anomalous diffusion of particles and structural phase transition in the system has been discussed.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.     

The influence of particle distribution and interphase on the thermal expansion coefficient of particulate composites by the use of a new model

In this work, the thermal expansion coefficient (CTE) of a composite containing spherical particles surrounded by an inhomogeneous interphase embedded in an isotropic matrix is evaluated by means of a new model. The thermomechanical properties of the interphase are formulated as continuous radial functions. It is assumed that this third phase developed between the polymeric matrix and the filler particles contains both areas of absorption interaction in polymer surface layers onto filler particles as well as areas of mechanical imperfections. It can be said that the concept of boundary interphase is a useful tool to describe quantitatively the adhesion efficiency between matrix and particles and that there is an effect of this phase on the thermomechanical properties of the composite. The thickness and volume fraction of this phase were determined from heat capacity measurements for various filler contents. On the other hand, it is assumed that the particle arrangement (distribution) which can be considered as an influence of neighboring inclusions and their interaction should affect the thermomechanical constants of the composite. The theoretical predictions were compared with experimental results as well as with theoretical values from expressions obtained from other workers and they were found to be in satisfactory agreement.     

Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin -1/2 particles with one of particles driven by rotating magnetic field. The influences of coupling and precession frequency of the magnetic field on geometric phase are also discussed in detail.     

Static Wiener spectrum of a thin film of polymer-encapsulated ferroelectric liquid crystals

Results of computer simulation of the shading effect in systems of opaque spherical particles scattering light in accordance with the Lambert law are presented. Two types of systems are studied: a semi-infinite medium and statistically uniform clusters of a finite number of particles. The simulation makes it possible to obtain photometric characteristics of systems with an accuracy better than 1%. The phase dependence of the shading effect is shown to become steeper as the packing density of particles in clusters decreases and their number increases. For statistically uniform media, the following relation takes place: The lower the packing density, the more pronounced the shadow decrease in brightness with an increasing phase angle.     

NaCl structure in a mixture of silica and gold sols

The formation of an NaCl structure in a mixture of a monodisperse silica sol with particle diameter of 5300 A and a gold sol with average particle size of 800 A is described. The mixture was left still for a month, and the particles settled to form a dense layer at the bottom, where phase separation appeared. In the ordered phase only gold particles were observed microscopically as bright spots at their individual lattice points, being arranged in hexagonal or in square pattern. From the distance between the particles in the square pattern and hexagonal pattern, the lattice type for gold particles was concluded to be fcc. Further, it was known that four gold particles forming a square hold one silica particle in its center. On these grounds, the entire lattice was concluded to be of the NaCl-type.     

Surface and bulk melting of small metal clusters

We present an analytical solution to the two-parabola Landau model, applied to melting of metal particles with sizes in the nanoscale range. The results provide an analytical understanding of the recently observed pseudo-crystalline phase of nanoscale Sn particles. Liquid skin formation as a precursor of melting is found to occur only for particles with radii greater than an explicitly given critical radius. The size dependences of the melting temperature, and of the latent heat, have been calculated, and a quantitative agreement is found with the experiment on tin particles.     

The Effect of Sphere Size on the Phase Behaviors in the Rod and Sphere Mixture System

The addition of polysaccharides, such as chondroitin sulfate (Chs), to the aqueous suspension of tobacco mosaic virus (TMV) results in the TMV aggregation at very dilute TMV concentration compared with the addition of polyethylene oxide (PEO). The Chs chain has a semirigid nature, whereas the PEO has a flexible nature. In this study, we investigated the effect of the size of spherical polymer coils on the phase behaviors in the mixtures of rods and spheres using Monte Carlo simulations. As a model for TMV, we used the spherocylinder particle. The Chs and PEO chains were simplified to spherical particles having different sizes. With the addition of large spherical particles, the system changed from miscible phase to isotropic–isotropic phase separation and then isotropic–nematic phase separation states, whereas with the addition of small spherical particles, the system transformed from miscible isotropic phase to miscible nematic phase. We found that the sphere size had an important influence on the phase behaviors in the mixtures of rods and spheres.     

Sizing of Irregular Particles Using a Phase Doppler System

Response of a phase Doppler system to irregularly shaped particles is examined and shown to deviate qualitatively as well as quantitatively from the spherical particles. Nevertheless, the measured phase distributions based on an ensemble of particles exhibit a high degree of order and simplicity. The experimental data and the stochastic modeling of the process have shown that the phase Doppler technique can be used successfully for in-situ sizing and velocimetry of irregular particles. In the case of irregular crystalline particles, mean size and standard deviation can be deduced without requiring any assumptions regarding the functional form of the size distribution. As opposed to other optical techniques, phase Doppler can be used, in principle, near the backscattering location, so that a single optical window would be employed for transmission of laser light and collection of the scattered signals. Furthermore, size measurements can be velocity-resolved, i.e. a size distribution can be associated with each bin of the velocity histogram.     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. II. The Charged System and the Two-Component Burgers Equations

We further study the stochastic model discussed in ref. 2 in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.     

Quantitative electron microprobe analysis of commercial microcrystalline phosphor powders

Quantitative chemical analysis of individual particles from three commercial willemite fluorescent lamp powders (Zn₂SiO₄:Mn) has been made using an electron microprobe. A simple interference type spectrometer attachment and photomultiplier readout also allowed simultaneous recording of cathodoluminescence spectra of individual particles. There is significant grain-to-grain variation in the Zn/Mn and Zn/Si ratios calibrated against single-crystal material. In addition to the usual green particles, occasional orange and blue luminescing particles are observed in all the samples studied. Spectra of orange particles, which had higher concentrations of Mn, show two broad bands with peaks around 5300 Å and 5900 Å. Comparison with single crystals, artificially doped with Mn, suggest that the orange particles have a second phase, with tephroite structure, present along with willemite phase. Mn²⁺ in tephroite is six-fold coordinated, thus luminescence emission from this phase would be in the red region in comparison to Mn²⁺ in the willemite structure where it is four-fold coordinated.     

Ratchet transport of self-propelled chimeras in an asymmetric periodic structure

We studied the rectified transport of underdamped particles subject to phase lag in an asymmetric periodic structure. When the inertia effect is considered, it is possible to observe reversals of the average velocity with small self-propelled force, whereas particles always move in the positive direction with large self-propelled force. The introduction of phase lag leads particles to follow circular orbits and suppress the polar motion. In addition, this can adjust the direction of particle motion. There exists an optimal value of polar interaction strength at which the rectification is maximal. These results open the way for many application processes, such as spatial sorting of particles mixture and separation based on their physical properties.     

Design of an Acoustic Levitator for Three-Dimensional Manipulation of Numerous Particles

We present a design of an acoustic levitator consisting of three pairs of opposite transducer arrays.Three orthogonal standing waves create a large number of acoustic traps at which the particles are levitated in mid-air.By changing the phase difference of transducer arrays,three-dimensional manipulation of particles is successfully realized.Moreover,the relationship between the translation of particles and the phase difference is experimentally investigated,and the result is in agreement with the theoretical calculation.This design can expand the application of acoustic levitation in many fields,such as biomedicine,ultrasonic motor and new materials processing.     

Optical properties of single mixed-phase aerosol particles

We examine the light scattering from wet aerosol particles whose core morphology is a random Gaussian sphere coated by different amounts of water. We compare the results with those calculated from a concentric-sphere particle and from a homogeneous-sphere particle whose refractive index is determined from the Bruggeman mixing rule. In nearly all cases the differences between those of the Gaussian-core and the concentric-sphere particles are small. The most significant differences are seen in calculations of the asymmetry parameters and the intensity and polarization phase functions. The results of the homogeneous-sphere particles vary significantly from those of the Gaussian-core particles, typically an order of magnitude greater than for the concentric-sphere particles. It is not uncommon to see differences of 10% in the efficiencies of large, homogeneous-sphere particles; whereas, in the intensity and polarization phase functions, differences of several tens of percent are not uncommon.     

Phase separation and structure in a concentrated colloidal dispersion of uniform plates

The structure and phase behaviour of a colloidal dispersion of plate-like particles are described. The plates are nickel (II) hydroxide and have short-range, repulsive interactions and a low polydispersity. As the concentration of the plates is increased, an equilibrium phase separation between a columnar phase and a less ordered phase is observed. Complementary measurements using small-angle neutron and small-angle X-ray scattering have been used to distinguish the columnar phase from other possible ordered structures. Previously isotropic-nematic phase transitions have been observed [#!ref1!#], however this dispersion forms the more highly ordered columnar phase, due to the aspect ratio and the low polydispersity of the plate-like particles. The concentration at which phase separation occurs, increases as the range of the particle interactions is reduced. This system provides an interesting model for comparison with theory and calculations of structures in liquid crystal and mesophase in which the particle interactions can be altered. Received 24 February 1999